I'd like to note that the prime "sieve" example that is sitting at the top of the homepage is not a real sieve [...]
My understanding is that it *is* a sieve, just not the Sieve of Eratosthenes (because it's a bit hard to fit that into that small little sample box up the top of the page :p).
The main characteristic of a sieve is that it does not divide and that it eliminates all multiples of a prime without a test. Check one bit, eliminate many. In general if you see any of `mod`, `div` and friends, then it's very unlikely to be a sieve. The only real advantage of the example is that it uses shared primes to use trial division only against primes (instead of probable primes). This gives a slight speedup at the expense of needing a lot of memory. Greets, Ertugrul